Low Emittance High Energy Gain Inverse Free Electron Laser Using a Waveguided Helical Undulator

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1 Low Emittance High Energy Gain Inverse Free Electron Laser Using a Wavegided Helical Undlator Matthew James Affolter Particle Beam Physics Laboratory, University of California at Los Angeles (Dated: September 5, 007) Abstract Free electron lasers (FEL) are capable of prodcing high brightness X-ray radiation bt reqire a high crrent and low emittance electron beam. Work is nderway at the UCLA Neptne laboratory to prodce sch a beam sing an inverse free electron laser (IFEL). Prodcing a high energy gain IFEL reqires a high power laser. De to the power limitations of the optics, the near-tw CO laser implemented by UCLA provides the needed power at the cost of a short Rayleigh length. After several modifications, inclding the addition of a wavegide to control the highly divergent laser beam, the helical ndlator design has been completed. This design is expected, from 1-D electron dynamic simlations, to prodce a 100 MeV electron beam with a trapping fraction of 63% and a normalized emittance of 5 mm-mrad. Introdction The FEL is a versatile laser with applications in a wide range of fields. Its high power, at a wide range of wavelengths from millimeters to X-rays, makes it the prime candidate for antimissile defense systems. Imaging of nanostrctres is also possible with this extraordinary laser de to its short wavelengths and picosecond laser plses that are able to image an object withot destrction [1]. None of the characteristics that make the FEL so versatile wold be possible withot a highly energetic, low emittance, electron beam. In fact, the advancement of the FEL is strongly dependent on the development of sperior electron accelerators. Advancements of the FEL have mainly occrred over the past decade with higher energy accelerators becoming more common. The first FEL developed by Dr. Madey in 1976, five years after he created the FEL theory, only amplified a 10 µm laser beam by a small amont. It took scientists nearly another two decades and a half a billion dollars from the government, who wanted to se the FEL as an antimissile defense system dring the Cold War, to prodce a sixth of the power of a standard light blb (11 W). Powerfl FELs cold not be created becase technology had not yet caght p with the physics. It was not ntil accelerators reached higher energies that tre advancements in FELs began. Althogh accelerators have been rapidly increasing in energy, the majority are large and expensive making them impractical for prodcing FEL. However, the IFEL is a new form of accelerator that promises to prodce a high acceleration gradient while remaining smaller than its conterparts. Generating sch a gradient with an IFEL reqires a powerfl laser and a strong ndlating magnetic field. The final design, along with the IFEL theory, the design process of the ndlator, inclding problems, simlations and modifications are presented in this paper [].

2 Figre 1: Diagram of the major components of the FEL in the oscillation scheme. Two mirrors form an optical resonator with a planar ndlator in the middle. The electron beam travels down the length of the ndlator prodcing radiation that forms the laser light. FEL Theory Free electron lasers consist of two main components; a relativistic electron beam and an ndlator. An ndlator is a series of magnets that form a sinsoidal magnetic field. De to the Lorenz force the electron beam begins to wiggle as it is injected into the ndlator (Figre 1). This p and down motion, as seen in the electrons frame, prodces dipole radiation becase the electrons are accelerating charged particles. This radiation is then Doppler shifted to higher freqencies or shorter wavelengths into the laboratory frame. The wavelength of the radiation that is prodced is dependent on the energy of the electron beam, magnetic field of the ndlator (B ), and ndlator period (λ ) [3]. " " = (1 + K )! Where eb! K = = 0.093B " mc ( KGass)! ( cm) The FEL can operate in three different lasing schemes: amplification, oscillation, and self amplified spontaneos emission (SASE). High power laser light in the X-ray wavelengths can only be created throgh operation in the SASE scheme. Operation in the other modes is not possible becase X-ray seeding lasers do not exist (amplification) and mirrors do not reflect X-ray wavelength light which are needed to form the optical resonator of the oscillation scheme. In the SASE scheme a long ndlator is sed. Radiation is prodced in the first section of the ndlator and is then amplified as it progresses along the remaining length. To prodce short X-ray wavelengths in this scheme the emittance (ε) of the electron beam mst follow this ineqality [4]. $ < 4!"# So by prodcing a low emittance electron beam it is possible to obtain short wavelength X-rays withot large expensive high energy accelerators. Figre : Snapshots of the electron and electric field of the laser as they progress along the length of an ndlator. This diagram is of a FEL since the wiggle velocity of the electron is in the same direction as the electric field of the laser. For an IFEL the electron wiggle velocity will be in the opposite direction.

3 IFEL Theory The inverse free electron laser, as the name implies, operates in the FEL laser amplification scheme bt in reverse. In the FEL laser amplification scheme, a seeding laser is injected along with the electron beam into the ndlator. If the electron wiggle velocity is in the same direction as the electric field of the laser (Figre ) then energy is transferred from the kinetic energy of the electron beam to the laser, and the laser is amplified. However, if the electric field and electron velocity are in opposite direction then energy is transferred from the laser to the electrons, casing the electrons to accelerate. So the IFEL is a FEL operating in the laser amplification scheme with the electron beam 180 degrees ot of phase. Net acceleration occrs when [5]: " " = (1 )! r + K The radiation wavelength (λ r ) is the wavelength of light that is being sed as the seeding laser. So the ndlator period (λ ) and magnetic field (B ) mst be chosen to satisfy the above condition. Design UCLA s IFEL is niqe in the high power laser that it employs. High acceleration gradients can be created sing the 10.6 µm CO laser able to prodce TW of power. A short Rayleigh length is the cost of this high power. Large mirrors, with small f/#, are reqired since the intensity of the light wold destroy smaller mirrors. The highly divergent laser beam, de to the short Rayleigh range, cased the laser and electron beam to be mismatched and prevented ideal electron acceleration in the previos designs. In the new IFEL design a wavegide is sed to control the divergent laser beam. Research has been condcted at UCLA to find the optimm wavegide for this sitation. To maintain the high acceleration gradient throghot the ndlator the wavegide mst not significantly attenate the laser. Capillary wavegides, hollow condcting cylinders, are the simplest form of wavegides. The power loss in these wavegides is cased by the power dissipated in the condcting walls from the indced crrents created by the magnetic field of the electromagnetic wave. The power loss in lower order modes for a copper wavegide is qite small. However, these wavegides can excite higher modes, in trn destroying the ideal electron acceleration scheme. An Open Iris-Loaded wavegide Strctre (OILS) has been fond to be the ideal wavegide for this sitation. The OILS is a cylindrical pipe with a series of irises along its length. In this strctre the laser beam is kept from diverging and has little interaction with the walls of the wavegide. Small amonts of attenation along with no excitation of higher modes makes this wavegide perfect for the UCLA IFEL. Prodcing a high acceleration gradient also reqires a strong precise magnetic field inside the ndlator. If the magnetic field is slightly flawed the electrons will not obtain the appropriate trajectory and peak acceleration will not occr. UCLA s ndlator design allows the individal magnets to be adjsted to create a nearly flawless field. Designing the ndlator to have a strong bt tnable magnetic field is challenging becase the magnets are created of Neodymim Iron Boron (NdFeB), which is a fairly brittle material. As sch, the magnets themselves can not be threaded

4 to be adjsted by a screw. Instead a holder mst be created for the magnets that will allow them to be adjsted. Several problems were encontered in the design of this holder. The holder itself mst be of simple design so it will be easy to machine. It mst be able to constrain the magnet from shear forces. It mst be designed so that the magnetic field remains as strong as possible by keeping the magnets close together. slightly tapered on one end. This barely affects the strength of the magnetic field, bt allows the magnets to be moved closer together, increasing the field. Figre 3: Simlation of the magnetic field of the UCLA ndlator sing Radia. The red plot is the magnetic field in the x-direction and the ble is the magnetic field in the z-direction. The strength of the magnetic field is the 0.1 T that is reqired for ideal electron acceleration. After three design modifications the magnet holder design is complete. Simlations were condcted on the static magnetic field that this design creates sing a program called Radia, created by the Eropean Synchrotron Radiation Facility (ESRF). From 1-D electron dynamic simlations it has been fond that to achieve strong bnching and a high acceleration gradient the magnetic field of the ndlator needs to be arond 0.1 T. By increasing the size of the magnets from the previos design to 11 x 11 x 3.6 mm the desired strength of the magnetic field is achieved, figre 3 is a graph of the simlated magnetic field. The magnet design was then improved pon frther. Instead of sing rectanglar magnets the magnets were Figre 4: Ideal bnching of the electron beam after it travels throgh the ndlator. Simlation prodced sing helical IFEL dynamic eqations. Using Mathematica, a Wolfram Research program, the bnching of the electron beam was investigated for the adjstable IFEL design parameters. In this design the laser intensity, magnetic field strength, and electron beam injection energy can all be slightly modified. If for some reason the bnching of the electron beam is not what we expect these parameters will be adjsted to remedy the sitation. The Mathematica program simlates the electron dynamics as the beam progresses throgh the ndlator. Figre 4 is a plot of the ideal bnching of the electron beam. By adjsting the parameters in the program it is possible to investigate how the bnching is affected (Table 1). Increase in Bnching o Increase in Laser Intensity o Increase in Electron Energy Decrease in Bnching o Undlator Period o Decrease in Laser Intensity o Decrease in Electron Energy Table 1: Affects of IFEL parameters on the bnching of the electron beam, sing 1-D

5 electron dynamic simlations. The ndlator that is now being constrcted is a smaller design of the 100 MeV. This design will not prodce electrons with energies of 100 MeV bt will test the type of acceleration gradient and bnching we shold expect. The final design will be abot eight times longer (80 cm) with a tapered period so that as the electrons increase in energy they will remain in phase with the lasers electric field. From 1-D simlations of this design we are expecting an electron beam with a high energy and low emittance. The exact beam characteristic that the simlation predicted is presented in Table. Normalized emittance (ε) 5 mm-mrad Matched rms beam size (σ) 175µm Injection energy 14.5 MeV Extraction energy 100 MeV Trapping fraction ~ 63% Table : Characteristics of the electron beam, fond throgh 1-D electron dynamic simlations, after exiting the UCLA 100 MeV IFEL. Conclsion In the next few months the prototype of the UCLA IFEL will be constrcted and tested. This test will demonstrate the acceleration gradient and bnching that the final design shold prodce. If the reslts of these tests are promising then the final design will be constrcted that shold prodce a 100 MeV low emittance electron beam. Acknowledgements I wold like to thank NSF for fnding this research, Dr. James Rosenzweig, Dr. Rodion Tikhoplav, UCLA, and Françoise Qéval for making this work possible. References 1. "DESY's free-electron laser FLASH illminates the nano-world." Photon Science. 19 Jan 007. HASYLAB. 11 Sep 007 <hasylab.desy.de/news events>.. Gover, Avraham. "Lasers: Free Electron Lasers."Encyclopedia of Modern Optics Pellegrini, Cladio. "Design considerations for a SASE X-ray FEL." Nclear Instrments and Methods in Physics Research (0001): O Shea, P.G., S.C. Bender, B.E. Carlsten, J. W. Early, D.W. Feldman, R.B. Feldman, W. J.D. Johnson, A.H. Lmpkin, R.L. Sheffield, R.W. Springer, W.E. Stein, L.M. Yong. "Performance Of The Photoinjector Accelerator For The Los Alamos Free-Electron Laser." IEEE (1991): Mrphy, Ryan. "Giding of a Plsed, Infrared CO Laser With an Open Iris-Loaded Wavegide Strctre." Rosenzweig, J., N. Bodzin, P. Frigola, C. Joshi, P. Msmeci, C. Pellegrini, S. Tochitsky, and G. Travish. "A Helical Undlator Wave-gide Inverse Free-Electron Laser." 1-8.